Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(521,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.521");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.l (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 882) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1097.5 | ||
Character | \(\chi\) | \(=\) | 2646.1097 |
Dual form | 2646.2.l.c.521.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.474556 | − | 0.821956i | −0.212228 | − | 0.367590i | 0.740183 | − | 0.672405i | \(-0.234739\pi\) |
−0.952412 | + | 0.304815i | \(0.901405\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.821956 | − | 0.474556i | 0.259925 | − | 0.150068i | ||||
\(11\) | 1.51873 | + | 0.876838i | 0.457914 | + | 0.264377i | 0.711167 | − | 0.703024i | \(-0.248167\pi\) |
−0.253253 | + | 0.967400i | \(0.581500\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.720756 | − | 0.416129i | −0.199902 | − | 0.115413i | 0.396708 | − | 0.917945i | \(-0.370153\pi\) |
−0.596610 | + | 0.802532i | \(0.703486\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.73638 | + | 4.73955i | 0.663670 | + | 1.14951i | 0.979644 | + | 0.200742i | \(0.0643352\pi\) |
−0.315975 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.21232 | − | 1.85463i | −0.736957 | − | 0.425482i | 0.0840051 | − | 0.996465i | \(-0.473229\pi\) |
−0.820962 | + | 0.570983i | \(0.806562\pi\) | |||||||
\(20\) | 0.474556 | + | 0.821956i | 0.106114 | + | 0.183795i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.876838 | + | 1.51873i | −0.186942 | + | 0.323794i | ||||
\(23\) | −0.888998 | + | 0.513263i | −0.185369 | + | 0.107023i | −0.589813 | − | 0.807540i | \(-0.700798\pi\) |
0.404444 | + | 0.914563i | \(0.367465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.04959 | − | 3.55000i | 0.409918 | − | 0.710000i | ||||
\(26\) | 0.416129 | − | 0.720756i | 0.0816096 | − | 0.141352i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.58867 | − | 3.80397i | 1.22348 | − | 0.706379i | 0.257826 | − | 0.966191i | \(-0.416994\pi\) |
0.965659 | + | 0.259812i | \(0.0836607\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 11.0016i | − | 1.97595i | −0.154602 | − | 0.987977i | \(-0.549409\pi\) | ||
0.154602 | − | 0.987977i | \(-0.450591\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.73955 | + | 2.73638i | −0.812826 | + | 0.469285i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.19830 | + | 3.80756i | −0.361398 | + | 0.625959i | −0.988191 | − | 0.153226i | \(-0.951034\pi\) |
0.626794 | + | 0.779185i | \(0.284367\pi\) | |||||||
\(38\) | 1.85463 | − | 3.21232i | 0.300861 | − | 0.521107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.821956 | + | 0.474556i | −0.129963 | + | 0.0750340i | ||||
\(41\) | −4.05647 | + | 7.02601i | −0.633514 | + | 1.09728i | 0.353314 | + | 0.935505i | \(0.385055\pi\) |
−0.986828 | + | 0.161774i | \(0.948278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08463 | + | 5.34273i | 0.470401 | + | 0.814759i | 0.999427 | − | 0.0338470i | \(-0.0107759\pi\) |
−0.529026 | + | 0.848606i | \(0.677443\pi\) | |||||||
\(44\) | −1.51873 | − | 0.876838i | −0.228957 | − | 0.132188i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.513263 | − | 0.888998i | −0.0756766 | − | 0.131076i | ||||
\(47\) | −6.80125 | −0.992064 | −0.496032 | − | 0.868304i | \(-0.665210\pi\) | ||||
−0.496032 | + | 0.868304i | \(0.665210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.55000 | + | 2.04959i | 0.502046 | + | 0.289856i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.720756 | + | 0.416129i | 0.0999509 | + | 0.0577067i | ||||
\(53\) | −1.88177 | + | 1.08644i | −0.258480 | + | 0.149234i | −0.623641 | − | 0.781711i | \(-0.714347\pi\) |
0.365161 | + | 0.930944i | \(0.381014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.66444i | − | 0.224433i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.80397 | + | 6.58867i | 0.499486 | + | 0.865134i | ||||
\(59\) | 10.8659 | 1.41462 | 0.707311 | − | 0.706902i | \(-0.249908\pi\) | ||||
0.707311 | + | 0.706902i | \(0.249908\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.09663i | − | 0.140409i | −0.997533 | − | 0.0702043i | \(-0.977635\pi\) | ||
0.997533 | − | 0.0702043i | \(-0.0223651\pi\) | |||||||
\(62\) | 11.0016 | 1.39721 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.789907i | 0.0979759i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.4481 | 1.76512 | 0.882559 | − | 0.470202i | \(-0.155819\pi\) | ||||
0.882559 | + | 0.470202i | \(0.155819\pi\) | |||||||
\(68\) | −2.73638 | − | 4.73955i | −0.331835 | − | 0.574755i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.0131i | − | 1.30701i | −0.756922 | − | 0.653505i | \(-0.773298\pi\) | ||
0.756922 | − | 0.653505i | \(-0.226702\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.16204 | − | 1.82561i | 0.370089 | − | 0.213671i | −0.303408 | − | 0.952861i | \(-0.598125\pi\) |
0.673497 | + | 0.739190i | \(0.264791\pi\) | |||||||
\(74\) | −3.80756 | − | 2.19830i | −0.442620 | − | 0.255547i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.21232 | + | 1.85463i | 0.368478 | + | 0.212741i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.84819 | 1.10801 | 0.554004 | − | 0.832514i | \(-0.313099\pi\) | ||||
0.554004 | + | 0.832514i | \(0.313099\pi\) | |||||||
\(80\) | −0.474556 | − | 0.821956i | −0.0530570 | − | 0.0918975i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.02601 | − | 4.05647i | −0.775893 | − | 0.447962i | ||||
\(83\) | −2.41103 | − | 4.17603i | −0.264645 | − | 0.458379i | 0.702825 | − | 0.711363i | \(-0.251922\pi\) |
−0.967471 | + | 0.252983i | \(0.918588\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.59713 | − | 4.49837i | 0.281699 | − | 0.487916i | ||||
\(86\) | −5.34273 | + | 3.08463i | −0.576121 | + | 0.332624i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.876838 | − | 1.51873i | 0.0934712 | − | 0.161897i | ||||
\(89\) | 2.15943 | − | 3.74024i | 0.228899 | − | 0.396465i | −0.728583 | − | 0.684957i | \(-0.759821\pi\) |
0.957482 | + | 0.288493i | \(0.0931541\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.888998 | − | 0.513263i | 0.0926845 | − | 0.0535114i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 6.80125i | − | 0.701495i | ||||||
\(95\) | 3.52051i | 0.361197i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.90396 | − | 2.25395i | 0.396387 | − | 0.228854i | −0.288537 | − | 0.957469i | \(-0.593169\pi\) |
0.684924 | + | 0.728615i | \(0.259836\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.04959 | + | 3.55000i | −0.204959 | + | 0.355000i | ||||
\(101\) | 6.33624 | − | 10.9747i | 0.630480 | − | 1.09202i | −0.356974 | − | 0.934114i | \(-0.616192\pi\) |
0.987454 | − | 0.157909i | \(-0.0504751\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.33341 | − | 4.23394i | 0.722582 | − | 0.417183i | −0.0931202 | − | 0.995655i | \(-0.529684\pi\) |
0.815702 | + | 0.578472i | \(0.196351\pi\) | |||||||
\(104\) | −0.416129 | + | 0.720756i | −0.0408048 | + | 0.0706760i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.08644 | − | 1.88177i | −0.105524 | − | 0.182773i | ||||
\(107\) | 1.28657 | + | 0.742804i | 0.124378 | + | 0.0718096i | 0.560898 | − | 0.827885i | \(-0.310456\pi\) |
−0.436520 | + | 0.899694i | \(0.643789\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.60276 | + | 13.1684i | 0.728213 | + | 1.26130i | 0.957638 | + | 0.287975i | \(0.0929820\pi\) |
−0.229425 | + | 0.973326i | \(0.573685\pi\) | |||||||
\(110\) | 1.66444 | 0.158698 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.0031 | + | 9.81676i | 1.59952 | + | 0.923483i | 0.991579 | + | 0.129501i | \(0.0413376\pi\) |
0.607941 | + | 0.793982i | \(0.291996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.843760 | + | 0.487145i | 0.0786810 | + | 0.0454265i | ||||
\(116\) | −6.58867 | + | 3.80397i | −0.611742 | + | 0.353190i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8659i | 1.00029i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.96231 | − | 6.86292i | −0.360210 | − | 0.623902i | ||||
\(122\) | 1.09663 | 0.0992838 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 11.0016i | 0.987977i | ||||||||
\(125\) | −8.63615 | −0.772441 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.7051 | 1.65981 | 0.829903 | − | 0.557907i | \(-0.188395\pi\) | ||||
0.829903 | + | 0.557907i | \(0.188395\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.789907 | −0.0692794 | ||||||||
\(131\) | 3.32193 | + | 5.75375i | 0.290238 | + | 0.502707i | 0.973866 | − | 0.227124i | \(-0.0729321\pi\) |
−0.683628 | + | 0.729831i | \(0.739599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.4481i | 1.24813i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.73955 | − | 2.73638i | 0.406413 | − | 0.234643i | ||||
\(137\) | 17.6798 | + | 10.2074i | 1.51049 | + | 0.872080i | 0.999925 | + | 0.0122395i | \(0.00389606\pi\) |
0.510562 | + | 0.859841i | \(0.329437\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.9829 | + | 6.34099i | 0.931559 | + | 0.537836i | 0.887304 | − | 0.461184i | \(-0.152575\pi\) |
0.0442550 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.0131 | 0.924196 | ||||||||
\(143\) | −0.729755 | − | 1.26397i | −0.0610252 | − | 0.105699i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.25339 | − | 3.61040i | −0.519316 | − | 0.299827i | ||||
\(146\) | 1.82561 | + | 3.16204i | 0.151088 | + | 0.261693i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.19830 | − | 3.80756i | 0.180699 | − | 0.312979i | ||||
\(149\) | −17.1827 | + | 9.92046i | −1.40767 | + | 0.812716i | −0.995163 | − | 0.0982404i | \(-0.968679\pi\) |
−0.412503 | + | 0.910956i | \(0.635345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.872422 | + | 1.51108i | −0.0709967 | + | 0.122970i | −0.899338 | − | 0.437253i | \(-0.855951\pi\) |
0.828342 | + | 0.560223i | \(0.189285\pi\) | |||||||
\(152\) | −1.85463 | + | 3.21232i | −0.150431 | + | 0.260553i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.04287 | + | 5.22090i | −0.726341 | + | 0.419353i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 9.49564i | − | 0.757835i | −0.925431 | − | 0.378917i | \(-0.876296\pi\) | ||
0.925431 | − | 0.378917i | \(-0.123704\pi\) | |||||||
\(158\) | 9.84819i | 0.783480i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.821956 | − | 0.474556i | 0.0649813 | − | 0.0375170i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.92061 | + | 10.2548i | −0.463738 | + | 0.803217i | −0.999144 | − | 0.0413777i | \(-0.986825\pi\) |
0.535406 | + | 0.844595i | \(0.320159\pi\) | |||||||
\(164\) | 4.05647 | − | 7.02601i | 0.316757 | − | 0.548639i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.17603 | − | 2.41103i | 0.324123 | − | 0.187133i | ||||
\(167\) | −1.73229 | + | 3.00041i | −0.134048 | + | 0.232179i | −0.925234 | − | 0.379398i | \(-0.876131\pi\) |
0.791185 | + | 0.611577i | \(0.209464\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.15367 | − | 10.6585i | −0.473359 | − | 0.819883i | ||||
\(170\) | 4.49837 | + | 2.59713i | 0.345009 | + | 0.199191i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.08463 | − | 5.34273i | −0.235201 | − | 0.407379i | ||||
\(173\) | −3.09982 | −0.235675 | −0.117838 | − | 0.993033i | \(-0.537596\pi\) | ||||
−0.117838 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.51873 | + | 0.876838i | 0.114478 | + | 0.0660941i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.74024 | + | 2.15943i | 0.280343 | + | 0.161856i | ||||
\(179\) | −0.500470 | + | 0.288947i | −0.0374069 | + | 0.0215969i | −0.518587 | − | 0.855025i | \(-0.673542\pi\) |
0.481180 | + | 0.876622i | \(0.340208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 26.0581i | − | 1.93688i | −0.249238 | − | 0.968442i | \(-0.580180\pi\) | ||
0.249238 | − | 0.968442i | \(-0.419820\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.513263 | + | 0.888998i | 0.0378383 | + | 0.0655378i | ||||
\(185\) | 4.17286 | 0.306795 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.59745i | 0.701835i | ||||||||
\(188\) | 6.80125 | 0.496032 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.52051 | −0.255405 | ||||||||
\(191\) | 1.77964i | 0.128770i | 0.997925 | + | 0.0643852i | \(0.0205086\pi\) | ||||
−0.997925 | + | 0.0643852i | \(0.979491\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.48335 | −0.106774 | −0.0533871 | − | 0.998574i | \(-0.517002\pi\) | ||||
−0.0533871 | + | 0.998574i | \(0.517002\pi\) | |||||||
\(194\) | 2.25395 | + | 3.90396i | 0.161824 | + | 0.280288i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.44809i | 0.174419i | 0.996190 | + | 0.0872096i | \(0.0277950\pi\) | ||||
−0.996190 | + | 0.0872096i | \(0.972205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.47403 | + | 5.46984i | −0.671596 | + | 0.387746i | −0.796681 | − | 0.604400i | \(-0.793413\pi\) |
0.125085 | + | 0.992146i | \(0.460080\pi\) | |||||||
\(200\) | −3.55000 | − | 2.04959i | −0.251023 | − | 0.144928i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.9747 | + | 6.33624i | 0.772177 | + | 0.445816i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.70010 | 0.537798 | ||||||||
\(206\) | 4.23394 | + | 7.33341i | 0.294993 | + | 0.510943i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.720756 | − | 0.416129i | −0.0499755 | − | 0.0288534i | ||||
\(209\) | −3.25243 | − | 5.63337i | −0.224975 | − | 0.389668i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7481 | − | 22.0804i | 0.877617 | − | 1.52008i | 0.0236678 | − | 0.999720i | \(-0.492466\pi\) |
0.853949 | − | 0.520357i | \(-0.174201\pi\) | |||||||
\(212\) | 1.88177 | − | 1.08644i | 0.129240 | − | 0.0746169i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.742804 | + | 1.28657i | −0.0507770 | + | 0.0879484i | ||||
\(215\) | 2.92766 | − | 5.07085i | 0.199665 | − | 0.345829i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.1684 | + | 7.60276i | −0.891875 | + | 0.514924i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.66444i | 0.112216i | ||||||||
\(221\) | − | 4.55475i | − | 0.306385i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3108 | + | 7.68501i | −0.891359 | + | 0.514626i | −0.874387 | − | 0.485230i | \(-0.838736\pi\) |
−0.0169720 | + | 0.999856i | \(0.505403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.81676 | + | 17.0031i | −0.653001 | + | 1.13103i | ||||
\(227\) | 4.17388 | − | 7.22937i | 0.277030 | − | 0.479830i | −0.693615 | − | 0.720346i | \(-0.743983\pi\) |
0.970645 | + | 0.240515i | \(0.0773165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3671 | − | 6.56281i | 0.751161 | − | 0.433683i | −0.0749523 | − | 0.997187i | \(-0.523880\pi\) |
0.826113 | + | 0.563504i | \(0.190547\pi\) | |||||||
\(230\) | −0.487145 | + | 0.843760i | −0.0321214 | + | 0.0556359i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.80397 | − | 6.58867i | −0.249743 | − | 0.432567i | ||||
\(233\) | −9.84350 | − | 5.68315i | −0.644869 | − | 0.372315i | 0.141619 | − | 0.989921i | \(-0.454769\pi\) |
−0.786488 | + | 0.617606i | \(0.788103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.22758 | + | 5.59033i | 0.210544 | + | 0.364673i | ||||
\(236\) | −10.8659 | −0.707311 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.67039 | − | 2.69645i | −0.302102 | − | 0.174419i | 0.341285 | − | 0.939960i | \(-0.389138\pi\) |
−0.643387 | + | 0.765541i | \(0.722471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.1233 | + | 6.99936i | 0.780928 | + | 0.450869i | 0.836759 | − | 0.547572i | \(-0.184448\pi\) |
−0.0558314 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(242\) | 6.86292 | − | 3.96231i | 0.441165 | − | 0.254707i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.09663i | 0.0702043i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.54353 | + | 2.67348i | 0.0982127 | + | 0.170109i | ||||
\(248\) | −11.0016 | −0.698605 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 8.63615i | − | 0.546198i | ||||||
\(251\) | −16.5094 | −1.04207 | −0.521033 | − | 0.853536i | \(-0.674453\pi\) | ||||
−0.521033 | + | 0.853536i | \(0.674453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80019 | −0.113177 | ||||||||
\(254\) | 18.7051i | 1.17366i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.06000 | + | 5.30007i | 0.190878 | + | 0.330610i | 0.945541 | − | 0.325502i | \(-0.105533\pi\) |
−0.754664 | + | 0.656112i | \(0.772200\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 0.789907i | − | 0.0489879i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.75375 | + | 3.32193i | −0.355468 | + | 0.205229i | ||||
\(263\) | 14.1668 | + | 8.17923i | 0.873565 | + | 0.504353i | 0.868531 | − | 0.495634i | \(-0.165064\pi\) |
0.00503369 | + | 0.999987i | \(0.498398\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.78601 | + | 1.03115i | 0.109714 | + | 0.0633432i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −14.4481 | −0.882559 | ||||||||
\(269\) | 2.65845 | + | 4.60457i | 0.162088 | + | 0.280745i | 0.935617 | − | 0.353015i | \(-0.114844\pi\) |
−0.773529 | + | 0.633761i | \(0.781510\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.2825 | + | 8.24602i | 0.867601 | + | 0.500910i | 0.866550 | − | 0.499090i | \(-0.166332\pi\) |
0.00105086 | + | 0.999999i | \(0.499666\pi\) | |||||||
\(272\) | 2.73638 | + | 4.73955i | 0.165917 | + | 0.287377i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.2074 | + | 17.6798i | −0.616654 | + | 1.06808i | ||||
\(275\) | 6.22554 | − | 3.59432i | 0.375414 | − | 0.216746i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.31402 | + | 12.6682i | −0.439457 | + | 0.761161i | −0.997648 | − | 0.0685513i | \(-0.978162\pi\) |
0.558191 | + | 0.829713i | \(0.311496\pi\) | |||||||
\(278\) | −6.34099 | + | 10.9829i | −0.380308 | + | 0.658712i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.62307 | + | 2.09178i | −0.216134 | + | 0.124785i | −0.604159 | − | 0.796864i | \(-0.706491\pi\) |
0.388025 | + | 0.921649i | \(0.373158\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.70591i | − | 0.576957i | −0.957486 | − | 0.288478i | \(-0.906851\pi\) | ||
0.957486 | − | 0.288478i | \(-0.0931493\pi\) | |||||||
\(284\) | 11.0131i | 0.653505i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.26397 | − | 0.729755i | 0.0747403 | − | 0.0431513i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.47555 | + | 11.2160i | −0.380915 | + | 0.659764i | ||||
\(290\) | 3.61040 | − | 6.25339i | 0.212010 | − | 0.367212i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.16204 | + | 1.82561i | −0.185045 | + | 0.106836i | ||||
\(293\) | −1.01377 | + | 1.75591i | −0.0592253 | + | 0.102581i | −0.894118 | − | 0.447832i | \(-0.852196\pi\) |
0.834893 | + | 0.550413i | \(0.185530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.15650 | − | 8.93131i | −0.300223 | − | 0.520001i | ||||
\(296\) | 3.80756 | + | 2.19830i | 0.221310 | + | 0.127773i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.92046 | − | 17.1827i | −0.574677 | − | 0.995370i | ||||
\(299\) | 0.854335 | 0.0494075 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.51108 | − | 0.872422i | −0.0869528 | − | 0.0502022i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.21232 | − | 1.85463i | −0.184239 | − | 0.106371i | ||||
\(305\) | −0.901378 | + | 0.520411i | −0.0516128 | + | 0.0297986i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.79004i | − | 0.558747i | −0.960183 | − | 0.279374i | \(-0.909873\pi\) | ||
0.960183 | − | 0.279374i | \(-0.0901268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.22090 | − | 9.04287i | −0.296527 | − | 0.513600i | ||||
\(311\) | −13.7039 | −0.777076 | −0.388538 | − | 0.921433i | \(-0.627020\pi\) | ||||
−0.388538 | + | 0.921433i | \(0.627020\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8585i | 1.06595i | 0.846132 | + | 0.532974i | \(0.178926\pi\) | ||||
−0.846132 | + | 0.532974i | \(0.821074\pi\) | |||||||
\(314\) | 9.49564 | 0.535870 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.84819 | −0.554004 | ||||||||
\(317\) | − | 7.86426i | − | 0.441701i | −0.975308 | − | 0.220850i | \(-0.929117\pi\) | ||
0.975308 | − | 0.220850i | \(-0.0708832\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.3419 | 0.747000 | ||||||||
\(320\) | 0.474556 | + | 0.821956i | 0.0265285 | + | 0.0459487i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.2999i | − | 1.12952i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.95451 | + | 1.70579i | −0.163887 | + | 0.0946202i | ||||
\(326\) | −10.2548 | − | 5.92061i | −0.567960 | − | 0.327912i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.02601 | + | 4.05647i | 0.387947 | + | 0.223981i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.7350 | 1.24963 | 0.624813 | − | 0.780774i | \(-0.285175\pi\) | ||||
0.624813 | + | 0.780774i | \(0.285175\pi\) | |||||||
\(332\) | 2.41103 | + | 4.17603i | 0.132323 | + | 0.229190i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.00041 | − | 1.73229i | −0.164175 | − | 0.0947866i | ||||
\(335\) | −6.85644 | − | 11.8757i | −0.374608 | − | 0.648839i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0639 | + | 17.4312i | −0.548217 | + | 0.949539i | 0.450180 | + | 0.892938i | \(0.351360\pi\) |
−0.998397 | + | 0.0566014i | \(0.981974\pi\) | |||||||
\(338\) | 10.6585 | − | 6.15367i | 0.579745 | − | 0.334716i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.59713 | + | 4.49837i | −0.140849 | + | 0.243958i | ||||
\(341\) | 9.64666 | − | 16.7085i | 0.522396 | − | 0.904816i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.34273 | − | 3.08463i | 0.288061 | − | 0.166312i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 3.09982i | − | 0.166647i | ||||||
\(347\) | − | 22.6395i | − | 1.21535i | −0.794185 | − | 0.607677i | \(-0.792102\pi\) | ||
0.794185 | − | 0.607677i | \(-0.207898\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.3378 | + | 7.70058i | −0.713955 | + | 0.412202i | −0.812524 | − | 0.582928i | \(-0.801907\pi\) |
0.0985684 | + | 0.995130i | \(0.468574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.876838 | + | 1.51873i | −0.0467356 | + | 0.0809485i | ||||
\(353\) | −15.6132 | + | 27.0429i | −0.831009 | + | 1.43935i | 0.0662300 | + | 0.997804i | \(0.478903\pi\) |
−0.897239 | + | 0.441545i | \(0.854430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.05225 | + | 5.22632i | −0.480444 | + | 0.277384i | ||||
\(356\) | −2.15943 | + | 3.74024i | −0.114449 | + | 0.198232i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.288947 | − | 0.500470i | −0.0152713 | − | 0.0264507i | ||||
\(359\) | −1.39179 | − | 0.803552i | −0.0734560 | − | 0.0424098i | 0.462822 | − | 0.886451i | \(-0.346837\pi\) |
−0.536278 | + | 0.844041i | \(0.680170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.62067 | − | 4.53913i | −0.137930 | − | 0.238902i | ||||
\(362\) | 26.0581 | 1.36958 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.00114 | − | 1.73271i | −0.157087 | − | 0.0906941i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.1877 | − | 9.34599i | −0.844992 | − | 0.487856i | 0.0139659 | − | 0.999902i | \(-0.495554\pi\) |
−0.858958 | + | 0.512046i | \(0.828888\pi\) | |||||||
\(368\) | −0.888998 | + | 0.513263i | −0.0463422 | + | 0.0267557i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.17286i | 0.216937i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.7682 | − | 32.5075i | −0.971781 | − | 1.68317i | −0.690173 | − | 0.723645i | \(-0.742465\pi\) |
−0.281609 | − | 0.959529i | \(-0.590868\pi\) | |||||||
\(374\) | −9.59745 | −0.496272 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.80125i | 0.350748i | ||||||||
\(377\) | −6.33177 | −0.326103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.63192 | −0.443392 | −0.221696 | − | 0.975116i | \(-0.571159\pi\) | ||||
−0.221696 | + | 0.975116i | \(0.571159\pi\) | |||||||
\(380\) | − | 3.52051i | − | 0.180599i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.77964 | −0.0910545 | ||||||||
\(383\) | 4.19997 | + | 7.27456i | 0.214608 | + | 0.371713i | 0.953151 | − | 0.302494i | \(-0.0978191\pi\) |
−0.738543 | + | 0.674206i | \(0.764486\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.48335i | − | 0.0755007i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.90396 | + | 2.25395i | −0.198193 | + | 0.114427i | ||||
\(389\) | −12.3475 | − | 7.12883i | −0.626043 | − | 0.361446i | 0.153175 | − | 0.988199i | \(-0.451050\pi\) |
−0.779218 | + | 0.626753i | \(0.784383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.86527 | − | 2.80897i | −0.246047 | − | 0.142056i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.44809 | −0.123333 | ||||||||
\(395\) | −4.67352 | − | 8.09477i | −0.235150 | − | 0.407292i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.2162 | − | 12.8265i | −1.11500 | − | 0.643744i | −0.174879 | − | 0.984590i | \(-0.555953\pi\) |
−0.940119 | + | 0.340846i | \(0.889287\pi\) | |||||||
\(398\) | −5.46984 | − | 9.47403i | −0.274178 | − | 0.474890i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.04959 | − | 3.55000i | 0.102480 | − | 0.177500i | ||||
\(401\) | −22.5981 | + | 13.0470i | −1.12849 | + | 0.651536i | −0.943556 | − | 0.331214i | \(-0.892542\pi\) |
−0.184938 | + | 0.982750i | \(0.559209\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.57810 | + | 7.92951i | −0.228052 | + | 0.394997i | ||||
\(404\) | −6.33624 | + | 10.9747i | −0.315240 | + | 0.546011i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.67722 | + | 3.85510i | −0.330978 | + | 0.191090i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.8308i | 1.52448i | 0.647292 | + | 0.762242i | \(0.275901\pi\) | ||||
−0.647292 | + | 0.762242i | \(0.724099\pi\) | |||||||
\(410\) | 7.70010i | 0.380281i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.33341 | + | 4.23394i | −0.361291 | + | 0.208591i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.28834 | + | 3.96353i | −0.112330 | + | 0.194562i | ||||
\(416\) | 0.416129 | − | 0.720756i | 0.0204024 | − | 0.0353380i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.63337 | − | 3.25243i | 0.275537 | − | 0.159081i | ||||
\(419\) | 13.9168 | − | 24.1047i | 0.679883 | − | 1.17759i | −0.295133 | − | 0.955456i | \(-0.595364\pi\) |
0.975016 | − | 0.222135i | \(-0.0713026\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.39960 | + | 12.8165i | 0.360634 | + | 0.624637i | 0.988065 | − | 0.154035i | \(-0.0492269\pi\) |
−0.627431 | + | 0.778672i | \(0.715894\pi\) | |||||||
\(422\) | 22.0804 | + | 12.7481i | 1.07486 | + | 0.620569i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.08644 | + | 1.88177i | 0.0527621 | + | 0.0913866i | ||||
\(425\) | 22.4339 | 1.08820 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.28657 | − | 0.742804i | −0.0621889 | − | 0.0359048i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.07085 | + | 2.92766i | 0.244538 | + | 0.141184i | ||||
\(431\) | 24.7338 | − | 14.2801i | 1.19139 | − | 0.687847i | 0.232765 | − | 0.972533i | \(-0.425223\pi\) |
0.958621 | + | 0.284686i | \(0.0918892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.0220i | − | 0.866080i | −0.901375 | − | 0.433040i | \(-0.857441\pi\) | ||
0.901375 | − | 0.433040i | \(-0.142559\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.60276 | − | 13.1684i | −0.364106 | − | 0.630651i | ||||
\(437\) | 3.80766 | 0.182145 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.5104i | 1.16982i | 0.811099 | + | 0.584909i | \(0.198870\pi\) | ||||
−0.811099 | + | 0.584909i | \(0.801130\pi\) | |||||||
\(440\) | −1.66444 | −0.0793489 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.55475 | 0.216647 | ||||||||
\(443\) | − | 10.5547i | − | 0.501469i | −0.968056 | − | 0.250734i | \(-0.919328\pi\) | ||
0.968056 | − | 0.250734i | \(-0.0806720\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.09908 | −0.194315 | ||||||||
\(446\) | −7.68501 | − | 13.3108i | −0.363896 | − | 0.630286i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.2540i | − | 0.814267i | −0.913369 | − | 0.407133i | \(-0.866528\pi\) | ||
0.913369 | − | 0.407133i | \(-0.133472\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.3213 | + | 7.11373i | −0.580190 | + | 0.334973i | ||||
\(452\) | −17.0031 | − | 9.81676i | −0.799760 | − | 0.461742i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.22937 | + | 4.17388i | 0.339291 | + | 0.195890i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.37536 | 0.0643368 | 0.0321684 | − | 0.999482i | \(-0.489759\pi\) | ||||
0.0321684 | + | 0.999482i | \(0.489759\pi\) | |||||||
\(458\) | 6.56281 | + | 11.3671i | 0.306660 | + | 0.531151i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.843760 | − | 0.487145i | −0.0393405 | − | 0.0227132i | ||||
\(461\) | 18.7031 | + | 32.3947i | 0.871088 | + | 1.50877i | 0.860872 | + | 0.508822i | \(0.169919\pi\) |
0.0102165 | + | 0.999948i | \(0.496748\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.18312 | + | 8.97742i | −0.240880 | + | 0.417216i | −0.960965 | − | 0.276669i | \(-0.910769\pi\) |
0.720085 | + | 0.693886i | \(0.244103\pi\) | |||||||
\(464\) | 6.58867 | − | 3.80397i | 0.305871 | − | 0.176595i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.68315 | − | 9.84350i | 0.263267 | − | 0.455991i | ||||
\(467\) | 18.1423 | − | 31.4234i | 0.839527 | − | 1.45410i | −0.0507637 | − | 0.998711i | \(-0.516166\pi\) |
0.890291 | − | 0.455393i | \(-0.150501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.59033 | + | 3.22758i | −0.257862 | + | 0.148877i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 10.8659i | − | 0.500145i | ||||||
\(473\) | 10.8189i | 0.497452i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.1679 | + | 7.60248i | −0.604184 | + | 0.348826i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.69645 | − | 4.67039i | 0.123333 | − | 0.213619i | ||||
\(479\) | −11.5975 | + | 20.0875i | −0.529905 | + | 0.917822i | 0.469487 | + | 0.882939i | \(0.344439\pi\) |
−0.999391 | + | 0.0348822i | \(0.988894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.16887 | − | 1.82955i | 0.144488 | − | 0.0834202i | ||||
\(482\) | −6.99936 | + | 12.1233i | −0.318812 | + | 0.552199i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.96231 | + | 6.86292i | 0.180105 | + | 0.311951i | ||||
\(485\) | −3.70529 | − | 2.13925i | −0.168249 | − | 0.0971385i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.3695 | − | 24.8887i | −0.651144 | − | 1.12781i | −0.982846 | − | 0.184430i | \(-0.940956\pi\) |
0.331701 | − | 0.943384i | \(-0.392377\pi\) | |||||||
\(488\) | −1.09663 | −0.0496419 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.0143 | − | 12.1326i | −0.948364 | − | 0.547538i | −0.0557919 | − | 0.998442i | \(-0.517768\pi\) |
−0.892572 | + | 0.450904i | \(0.851102\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0582 | + | 20.8182i | 1.62398 | + | 0.937605i | ||||
\(494\) | −2.67348 | + | 1.54353i | −0.120285 | + | 0.0694468i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 11.0016i | − | 0.493988i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2911 | − | 23.0209i | −0.594992 | − | 1.03056i | −0.993548 | − | 0.113412i | \(-0.963822\pi\) |
0.398556 | − | 0.917144i | \(-0.369511\pi\) | |||||||
\(500\) | 8.63615 | 0.386221 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 16.5094i | − | 0.736852i | ||||||
\(503\) | 33.9478 | 1.51366 | 0.756829 | − | 0.653613i | \(-0.226748\pi\) | ||||
0.756829 | + | 0.653613i | \(0.226748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0276 | −0.535222 | ||||||||
\(506\) | − | 1.80019i | − | 0.0800284i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.7051 | −0.829903 | ||||||||
\(509\) | 5.70574 | + | 9.88263i | 0.252902 | + | 0.438040i | 0.964324 | − | 0.264726i | \(-0.0852815\pi\) |
−0.711421 | + | 0.702766i | \(0.751948\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.30007 | + | 3.06000i | −0.233776 | + | 0.134971i | ||||
\(515\) | −6.96023 | − | 4.01849i | −0.306704 | − | 0.177076i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3292 | − | 5.96359i | −0.454280 | − | 0.262278i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.789907 | 0.0346397 | ||||||||
\(521\) | −9.24387 | − | 16.0108i | −0.404981 | − | 0.701448i | 0.589338 | − | 0.807887i | \(-0.299389\pi\) |
−0.994319 | + | 0.106439i | \(0.966055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.133147 | − | 0.0768726i | −0.00582212 | − | 0.00336140i | 0.497086 | − | 0.867701i | \(-0.334403\pi\) |
−0.502908 | + | 0.864340i | \(0.667737\pi\) | |||||||
\(524\) | −3.32193 | − | 5.75375i | −0.145119 | − | 0.251354i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.17923 | + | 14.1668i | −0.356631 | + | 0.617704i | ||||
\(527\) | 52.1428 | − | 30.1047i | 2.27138 | − | 1.31138i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9731 | + | 19.0060i | −0.477092 | + | 0.826348i | ||||
\(530\) | −1.03115 | + | 1.78601i | −0.0447904 | + | 0.0775792i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.84746 | − | 3.37603i | 0.253281 | − | 0.146232i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.41001i | − | 0.0609600i | ||||||
\(536\) | − | 14.4481i | − | 0.624063i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.60457 | + | 2.65845i | −0.198517 | + | 0.114614i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.9635 | − | 31.1136i | 0.772309 | − | 1.33768i | −0.163985 | − | 0.986463i | \(-0.552435\pi\) |
0.936294 | − | 0.351216i | \(-0.114232\pi\) | |||||||
\(542\) | −8.24602 | + | 14.2825i | −0.354197 | + | 0.613487i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.73955 | + | 2.73638i | −0.203206 | + | 0.117321i | ||||
\(545\) | 7.21588 | − | 12.4983i | 0.309094 | − | 0.535367i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2216 | + | 17.7043i | 0.437044 | + | 0.756983i | 0.997460 | − | 0.0712286i | \(-0.0226920\pi\) |
−0.560416 | + | 0.828211i | \(0.689359\pi\) | |||||||
\(548\) | −17.6798 | − | 10.2074i | −0.755244 | − | 0.436040i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.59432 | + | 6.22554i | 0.153262 | + | 0.265458i | ||||
\(551\) | −28.2199 | −1.20221 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −12.6682 | − | 7.31402i | −0.538222 | − | 0.310743i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.9829 | − | 6.34099i | −0.465780 | − | 0.268918i | ||||
\(557\) | −18.8181 | + | 10.8646i | −0.797348 | + | 0.460349i | −0.842543 | − | 0.538629i | \(-0.818942\pi\) |
0.0451952 | + | 0.998978i | \(0.485609\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.13441i | − | 0.217162i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.09178 | − | 3.62307i | −0.0882365 | − | 0.152830i | ||||
\(563\) | −20.8519 | −0.878805 | −0.439402 | − | 0.898290i | \(-0.644810\pi\) | ||||
−0.439402 | + | 0.898290i | \(0.644810\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 18.6344i | − | 0.783957i | ||||||
\(566\) | 9.70591 | 0.407970 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.0131 | −0.462098 | ||||||||
\(569\) | − | 11.6914i | − | 0.490128i | −0.969507 | − | 0.245064i | \(-0.921191\pi\) | ||
0.969507 | − | 0.245064i | \(-0.0788090\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.5544 | 0.567235 | 0.283617 | − | 0.958938i | \(-0.408465\pi\) | ||||
0.283617 | + | 0.958938i | \(0.408465\pi\) | |||||||
\(572\) | 0.729755 | + | 1.26397i | 0.0305126 | + | 0.0528494i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.20792i | 0.175483i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.0748 | + | 11.5902i | −0.835727 | + | 0.482507i | −0.855809 | − | 0.517291i | \(-0.826940\pi\) |
0.0200828 | + | 0.999798i | \(0.493607\pi\) | |||||||
\(578\) | −11.2160 | − | 6.47555i | −0.466523 | − | 0.269347i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.25339 | + | 3.61040i | 0.259658 | + | 0.149914i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.81052 | −0.157816 | ||||||||
\(584\) | −1.82561 | − | 3.16204i | −0.0755442 | − | 0.130846i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.75591 | − | 1.01377i | −0.0725358 | − | 0.0418786i | ||||
\(587\) | −4.22194 | − | 7.31262i | −0.174258 | − | 0.301824i | 0.765646 | − | 0.643262i | \(-0.222419\pi\) |
−0.939904 | + | 0.341438i | \(0.889086\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.4040 | + | 35.3408i | −0.840733 | + | 1.45619i | ||||
\(590\) | 8.93131 | − | 5.15650i | 0.367696 | − | 0.212290i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.19830 | + | 3.80756i | −0.0903494 | + | 0.156490i | ||||
\(593\) | −16.3255 | + | 28.2765i | −0.670407 | + | 1.16118i | 0.307382 | + | 0.951586i | \(0.400547\pi\) |
−0.977789 | + | 0.209592i | \(0.932786\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17.1827 | − | 9.92046i | 0.703833 | − | 0.406358i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.854335i | 0.0349364i | ||||||||
\(599\) | − | 47.9900i | − | 1.96082i | −0.196974 | − | 0.980409i | \(-0.563112\pi\) | ||
0.196974 | − | 0.980409i | \(-0.436888\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.1783 | + | 11.6499i | −0.823090 | + | 0.475211i | −0.851481 | − | 0.524386i | \(-0.824295\pi\) |
0.0283909 | + | 0.999597i | \(0.490962\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.872422 | − | 1.51108i | 0.0354983 | − | 0.0614849i | ||||
\(605\) | −3.76068 | + | 6.51369i | −0.152893 | + | 0.264819i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.3385 | − | 12.3198i | 0.866101 | − | 0.500044i | 5.03773e−5 | − | 1.00000i | \(-0.499984\pi\) |
0.866051 | + | 0.499956i | \(0.166651\pi\) | |||||||
\(608\) | 1.85463 | − | 3.21232i | 0.0752153 | − | 0.130277i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.520411 | − | 0.901378i | −0.0210708 | − | 0.0364957i | ||||
\(611\) | 4.90204 | + | 2.83020i | 0.198315 | + | 0.114497i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.2009 | − | 29.7928i | −0.694736 | − | 1.20332i | −0.970270 | − | 0.242027i | \(-0.922188\pi\) |
0.275533 | − | 0.961291i | \(-0.411146\pi\) | |||||||
\(614\) | 9.79004 | 0.395094 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.4321 | + | 12.9512i | 0.903083 | + | 0.521395i | 0.878199 | − | 0.478295i | \(-0.158745\pi\) |
0.0248838 | + | 0.999690i | \(0.492078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.1907 | − | 5.88361i | −0.409599 | − | 0.236482i | 0.281018 | − | 0.959702i | \(-0.409328\pi\) |
−0.690618 | + | 0.723220i | \(0.742661\pi\) | |||||||
\(620\) | 9.04287 | − | 5.22090i | 0.363170 | − | 0.209676i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 13.7039i | − | 0.549476i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.14962 | − | 10.6515i | −0.245985 | − | 0.426058i | ||||
\(626\) | −18.8585 | −0.753739 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.49564i | 0.378917i | ||||||||
\(629\) | −24.0615 | −0.959394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4353 | 0.654277 | 0.327139 | − | 0.944976i | \(-0.393916\pi\) | ||||
0.327139 | + | 0.944976i | \(0.393916\pi\) | |||||||
\(632\) | − | 9.84819i | − | 0.391740i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.86426 | 0.312329 | ||||||||
\(635\) | −8.87661 | − | 15.3747i | −0.352258 | − | 0.610128i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.3419i | 0.528209i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.821956 | + | 0.474556i | −0.0324907 | + | 0.0187585i | ||||
\(641\) | 13.4048 | + | 7.73929i | 0.529460 | + | 0.305684i | 0.740796 | − | 0.671730i | \(-0.234448\pi\) |
−0.211337 | + | 0.977413i | \(0.567782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.28185 | + | 1.89478i | 0.129423 | + | 0.0747226i | 0.563314 | − | 0.826243i | \(-0.309526\pi\) |
−0.433890 | + | 0.900966i | \(0.642860\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.2999 | 0.798690 | ||||||||
\(647\) | −11.0730 | − | 19.1789i | −0.435323 | − | 0.754002i | 0.561999 | − | 0.827138i | \(-0.310033\pi\) |
−0.997322 | + | 0.0731360i | \(0.976699\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.5024 | + | 9.52765i | 0.647775 | + | 0.373993i | ||||
\(650\) | −1.70579 | − | 2.95451i | −0.0669066 | − | 0.115886i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.92061 | − | 10.2548i | 0.231869 | − | 0.401609i | ||||
\(653\) | 6.54842 | − | 3.78073i | 0.256259 | − | 0.147951i | −0.366368 | − | 0.930470i | \(-0.619399\pi\) |
0.622627 | + | 0.782519i | \(0.286065\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.15289 | − | 5.46096i | 0.123193 | − | 0.213377i | ||||
\(656\) | −4.05647 | + | 7.02601i | −0.158379 | + | 0.274320i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.2514 | − | 7.07334i | 0.477246 | − | 0.275538i | −0.242022 | − | 0.970271i | \(-0.577811\pi\) |
0.719268 | + | 0.694733i | \(0.244477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.9586i | 0.892985i | 0.894787 | + | 0.446492i | \(0.147327\pi\) | ||||
−0.894787 | + | 0.446492i | \(0.852673\pi\) | |||||||
\(662\) | 22.7350i | 0.883620i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.17603 | + | 2.41103i | −0.162062 | + | 0.0935663i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.90488 | + | 6.76344i | −0.151197 | + | 0.261882i | ||||
\(668\) | 1.73229 | − | 3.00041i | 0.0670242 | − | 0.116089i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.8757 | − | 6.85644i | 0.458799 | − | 0.264888i | ||||
\(671\) | 0.961563 | − | 1.66548i | 0.0371207 | − | 0.0642950i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.86542 | − | 3.23100i | −0.0719066 | − | 0.124546i | 0.827830 | − | 0.560979i | \(-0.189575\pi\) |
−0.899737 | + | 0.436433i | \(0.856242\pi\) | |||||||
\(674\) | −17.4312 | − | 10.0639i | −0.671426 | − | 0.387648i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.15367 | + | 10.6585i | 0.236680 | + | 0.409941i | ||||
\(677\) | −47.5314 | −1.82678 | −0.913390 | − | 0.407087i | \(-0.866545\pi\) | ||||
−0.913390 | + | 0.407087i | \(0.866545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −4.49837 | − | 2.59713i | −0.172505 | − | 0.0995955i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.7085 | + | 9.64666i | 0.639802 | + | 0.369390i | ||||
\(683\) | −28.5275 | + | 16.4704i | −1.09158 | + | 0.630222i | −0.933996 | − | 0.357284i | \(-0.883703\pi\) |
−0.157580 | + | 0.987506i | \(0.550369\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 19.3760i | − | 0.740320i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.08463 | + | 5.34273i | 0.117600 | + | 0.203690i | ||||
\(689\) | 1.80839 | 0.0688943 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 7.93611i | − | 0.301904i | −0.988541 | − | 0.150952i | \(-0.951766\pi\) | ||
0.988541 | − | 0.150952i | \(-0.0482339\pi\) | |||||||
\(692\) | 3.09982 | 0.117838 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.6395 | 0.859385 | ||||||||
\(695\) | − | 12.0366i | − | 0.456576i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.4002 | −1.68178 | ||||||||
\(698\) | −7.70058 | − | 13.3378i | −0.291471 | − | 0.504843i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1838i | 0.951180i | 0.879667 | + | 0.475590i | \(0.157765\pi\) | ||||
−0.879667 | + | 0.475590i | \(0.842235\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.1233 | − | 8.15406i | 0.532669 | − | 0.307536i | ||||
\(704\) | −1.51873 | − | 0.876838i | −0.0572392 | − | 0.0330471i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −27.0429 | − | 15.6132i | −1.01777 | − | 0.587612i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.5021 | 0.807530 | 0.403765 | − | 0.914863i | \(-0.367701\pi\) | ||||
0.403765 | + | 0.914863i | \(0.367701\pi\) | |||||||
\(710\) | −5.22632 | − | 9.05225i | −0.196140 | − | 0.339725i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.74024 | − | 2.15943i | −0.140171 | − | 0.0809280i | ||||
\(713\) | 5.64674 | + | 9.78044i | 0.211472 | + | 0.366280i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.692620 | + | 1.19965i | −0.0259025 | + | 0.0448645i | ||||
\(716\) | 0.500470 | − | 0.288947i | 0.0187035 | − | 0.0107984i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.803552 | − | 1.39179i | 0.0299883 | − | 0.0519412i | ||||
\(719\) | −8.30671 | + | 14.3876i | −0.309788 | + | 0.536569i | −0.978316 | − | 0.207119i | \(-0.933591\pi\) |
0.668528 | + | 0.743687i | \(0.266925\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.53913 | − | 2.62067i | 0.168929 | − | 0.0975312i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.0581i | 0.968442i | ||||||||
\(725\) | − | 31.1863i | − | 1.15823i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.4866 | − | 22.7976i | 1.46448 | − | 0.845517i | 0.465265 | − | 0.885171i | \(-0.345959\pi\) |
0.999213 | + | 0.0396542i | \(0.0126256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.73271 | − | 3.00114i | 0.0641304 | − | 0.111077i | ||||
\(731\) | −16.8814 | + | 29.2395i | −0.624382 | + | 1.08146i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.3262 | − | 8.27123i | 0.529150 | − | 0.305505i | −0.211520 | − | 0.977374i | \(-0.567841\pi\) |
0.740670 | + | 0.671869i | \(0.234508\pi\) | |||||||
\(734\) | 9.34599 | − | 16.1877i | 0.344967 | − | 0.597500i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.513263 | − | 0.888998i | −0.0189191 | − | 0.0327689i | ||||
\(737\) | 21.9427 | + | 12.6686i | 0.808271 | + | 0.466656i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.75506 | + | 13.4322i | 0.285274 | + | 0.494110i | 0.972676 | − | 0.232168i | \(-0.0745819\pi\) |
−0.687401 | + | 0.726278i | \(0.741249\pi\) | |||||||
\(740\) | −4.17286 | −0.153397 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.0654 | − | 20.8224i | −1.32311 | − | 0.763899i | −0.338888 | − | 0.940827i | \(-0.610051\pi\) |
−0.984224 | + | 0.176928i | \(0.943384\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3084 | + | 9.41564i | 0.597492 | + | 0.344962i | ||||
\(746\) | 32.5075 | − | 18.7682i | 1.19018 | − | 0.687153i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 9.59745i | − | 0.350917i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.21569 | + | 10.7659i | 0.226814 | + | 0.392853i | 0.956862 | − | 0.290543i | \(-0.0938359\pi\) |
−0.730048 | + | 0.683395i | \(0.760503\pi\) | |||||||
\(752\) | −6.80125 | −0.248016 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 6.33177i | − | 0.230589i | ||||||
\(755\) | 1.65605 | 0.0602699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.8661 | 0.903775 | 0.451887 | − | 0.892075i | \(-0.350751\pi\) | ||||
0.451887 | + | 0.892075i | \(0.350751\pi\) | |||||||
\(758\) | − | 8.63192i | − | 0.313526i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.52051 | 0.127702 | ||||||||
\(761\) | 5.68277 | + | 9.84285i | 0.206000 | + | 0.356803i | 0.950451 | − | 0.310874i | \(-0.100622\pi\) |
−0.744451 | + | 0.667678i | \(0.767289\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 1.77964i | − | 0.0643852i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.27456 | + | 4.19997i | −0.262841 | + | 0.151751i | ||||
\(767\) | −7.83169 | − | 4.52163i | −0.282786 | − | 0.163266i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.8857 | + | 17.2545i | 1.07771 | + | 0.622214i | 0.930277 | − | 0.366859i | \(-0.119567\pi\) |
0.147429 | + | 0.989073i | \(0.452900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.48335 | 0.0533871 | ||||||||
\(773\) | 10.6262 | + | 18.4051i | 0.382197 | + | 0.661984i | 0.991376 | − | 0.131048i | \(-0.0418344\pi\) |
−0.609179 | + | 0.793033i | \(0.708501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39.0558 | − | 22.5489i | −1.40293 | − | 0.809980i | ||||
\(776\) | −2.25395 | − | 3.90396i | −0.0809121 | − | 0.140144i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.12883 | − | 12.3475i | 0.255581 | − | 0.442679i | ||||
\(779\) | 26.0614 | − | 15.0465i | 0.933745 | − | 0.539098i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.65667 | − | 16.7258i | 0.345543 | − | 0.598498i | ||||
\(782\) | 2.80897 | − | 4.86527i | 0.100448 | − | 0.173982i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.80500 | + | 4.50622i | −0.278572 | + | 0.160834i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.9663i | 0.426551i | 0.976992 | + | 0.213276i | \(0.0684132\pi\) | ||||
−0.976992 | + | 0.213276i | \(0.931587\pi\) | |||||||
\(788\) | − | 2.44809i | − | 0.0872096i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.09477 | − | 4.67352i | 0.287999 | − | 0.166276i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.456338 | + | 0.790400i | −0.0162050 | + | 0.0280679i | ||||
\(794\) | 12.8265 | − | 22.2162i | 0.455196 | − | 0.788422i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.47403 | − | 5.46984i | 0.335798 | − | 0.193873i | ||||
\(797\) | 2.86820 | − | 4.96786i | 0.101597 | − | 0.175971i | −0.810746 | − | 0.585398i | \(-0.800938\pi\) |
0.912343 | + | 0.409427i | \(0.134272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.6108 | − | 32.2348i | −0.658403 | − | 1.14039i | ||||
\(800\) | 3.55000 | + | 2.04959i | 0.125511 | + | 0.0724640i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.0470 | − | 22.5981i | −0.460706 | − | 0.797966i | ||||
\(803\) | 6.40305 | 0.225959 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.92951 | − | 4.57810i | −0.279305 | − | 0.161257i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.9747 | − | 6.33624i | −0.386088 | − | 0.222908i | ||||
\(809\) | −27.5185 | + | 15.8878i | −0.967500 | + | 0.558586i | −0.898473 | − | 0.439028i | \(-0.855323\pi\) |
−0.0690269 | + | 0.997615i | \(0.521989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.2541i | 1.44863i | 0.689471 | + | 0.724314i | \(0.257843\pi\) | ||||
−0.689471 | + | 0.724314i | \(0.742157\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.85510 | − | 6.67722i | −0.135121 | − | 0.234037i | ||||
\(815\) | 11.2386 | 0.393673 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 22.8834i | − | 0.800589i | ||||||
\(818\) | −30.8308 | −1.07797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.70010 | −0.268899 | ||||||||
\(821\) | − | 13.5045i | − | 0.471309i | −0.971837 | − | 0.235655i | \(-0.924277\pi\) | ||
0.971837 | − | 0.235655i | \(-0.0757234\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.9133 | −0.659277 | −0.329638 | − | 0.944107i | \(-0.606927\pi\) | ||||
−0.329638 | + | 0.944107i | \(0.606927\pi\) | |||||||
\(824\) | −4.23394 | − | 7.33341i | −0.147496 | − | 0.255471i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.8495i | 1.17706i | 0.808475 | + | 0.588531i | \(0.200293\pi\) | ||||
−0.808475 | + | 0.588531i | \(0.799707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8963 | + | 12.6418i | −0.760489 | + | 0.439068i | −0.829471 | − | 0.558550i | \(-0.811358\pi\) |
0.0689825 | + | 0.997618i | \(0.478025\pi\) | |||||||
\(830\) | −3.96353 | − | 2.28834i | −0.137576 | − | 0.0794296i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.720756 | + | 0.416129i | 0.0249877 | + | 0.0144267i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.28827 | 0.113795 | ||||||||
\(836\) | 3.25243 | + | 5.63337i | 0.112487 | + | 0.194834i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.1047 | + | 13.9168i | 0.832683 | + | 0.480750i | ||||
\(839\) | 1.28248 | + | 2.22133i | 0.0442763 | + | 0.0766888i | 0.887314 | − | 0.461165i | \(-0.152568\pi\) |
−0.843038 | + | 0.537854i | \(0.819235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4404 | − | 25.0114i | 0.497943 | − | 0.862463i | ||||
\(842\) | −12.8165 | + | 7.39960i | −0.441685 | + | 0.255007i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.7481 | + | 22.0804i | −0.438808 | + | 0.760038i | ||||
\(845\) | −5.84053 | + | 10.1161i | −0.200920 | + | 0.348004i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.88177 | + | 1.08644i | −0.0646201 | + | 0.0373084i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.4339i | 0.769475i | ||||||||
\(851\) | − | 4.51322i | − | 0.154711i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.98108 | − | 1.14378i | 0.0678310 | − | 0.0391622i | −0.465701 | − | 0.884942i | \(-0.654198\pi\) |
0.533532 | + | 0.845780i | \(0.320864\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.742804 | − | 1.28657i | 0.0253885 | − | 0.0439742i | ||||
\(857\) | 10.3313 | − | 17.8943i | 0.352911 | − | 0.611259i | −0.633847 | − | 0.773458i | \(-0.718525\pi\) |
0.986758 | + | 0.162199i | \(0.0518586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.3879 | + | 8.30688i | −0.490910 | + | 0.283427i | −0.724952 | − | 0.688800i | \(-0.758138\pi\) |
0.234042 | + | 0.972226i | \(0.424805\pi\) | |||||||
\(860\) | −2.92766 | + | 5.07085i | −0.0998323 | + | 0.172915i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.2801 | + | 24.7338i | 0.486381 | + | 0.842437i | ||||
\(863\) | 5.54125 | + | 3.19924i | 0.188626 | + | 0.108904i | 0.591339 | − | 0.806423i | \(-0.298599\pi\) |
−0.402713 | + | 0.915326i | \(0.631933\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.47104 | + | 2.54792i | 0.0500169 | + | 0.0866318i | ||||
\(866\) | 18.0220 | 0.612411 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.9567 | + | 8.63526i | 0.507372 | + | 0.292931i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4136 | − | 6.01228i | −0.352850 | − | 0.203718i | ||||
\(872\) | 13.1684 | − | 7.60276i | 0.445937 | − | 0.257462i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.80766i | 0.128796i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.08369 | − | 8.80522i | −0.171664 | − | 0.297331i | 0.767338 | − | 0.641243i | \(-0.221581\pi\) |
−0.939002 | + | 0.343912i | \(0.888248\pi\) | |||||||
\(878\) | −24.5104 | −0.827187 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 1.66444i | − | 0.0561081i | ||||||
\(881\) | −47.2933 | −1.59335 | −0.796675 | − | 0.604407i | \(-0.793410\pi\) | ||||
−0.796675 | + | 0.604407i | \(0.793410\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5706 | −0.557645 | −0.278822 | − | 0.960343i | \(-0.589944\pi\) | ||||
−0.278822 | + | 0.960343i | \(0.589944\pi\) | |||||||
\(884\) | 4.55475i | 0.153193i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.5547 | 0.354592 | ||||||||
\(887\) | 11.3965 | + | 19.7393i | 0.382656 | + | 0.662780i | 0.991441 | − | 0.130556i | \(-0.0416761\pi\) |
−0.608785 | + | 0.793335i | \(0.708343\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 4.09908i | − | 0.137402i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.3108 | − | 7.68501i | 0.445679 | − | 0.257313i | ||||
\(893\) | 21.8478 | + | 12.6138i | 0.731108 | + | 0.422105i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.475003 | + | 0.274243i | 0.0158776 | + | 0.00916694i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.2540 | 0.575774 | ||||||||
\(899\) | −41.8499 | − | 72.4862i | −1.39577 | − | 2.41755i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.2985 | − | 5.94581i | −0.343091 | − | 0.198084i | ||||
\(902\) | −7.11373 | − | 12.3213i | −0.236861 | − | 0.410256i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.81676 | − | 17.0031i | 0.326501 | − | 0.565516i | ||||
\(905\) | −21.4186 | + | 12.3660i | −0.711979 | + | 0.411061i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0653 | − | 41.6824i | 0.799077 | − | 1.38404i | −0.121142 | − | 0.992635i | \(-0.538656\pi\) |
0.920218 | − | 0.391406i | \(-0.128011\pi\) | |||||||
\(908\) | −4.17388 | + | 7.22937i | −0.138515 | + | 0.239915i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.5958 | + | 11.8910i | −0.682368 | + | 0.393966i | −0.800747 | − | 0.599003i | \(-0.795564\pi\) |
0.118378 | + | 0.992969i | \(0.462230\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.45635i | − | 0.279864i | ||||||
\(914\) | 1.37536i | 0.0454930i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.3671 | + | 6.56281i | −0.375580 | + | 0.216841i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.9692 | + | 18.9992i | −0.361841 | + | 0.626727i | −0.988264 | − | 0.152757i | \(-0.951185\pi\) |
0.626423 | + | 0.779483i | \(0.284518\pi\) | |||||||
\(920\) | 0.487145 | − | 0.843760i | 0.0160607 | − | 0.0278179i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.3947 | + | 18.7031i | −1.06686 | + | 0.615953i | ||||
\(923\) | −4.58286 | + | 7.93774i | −0.150847 | + | 0.261274i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.01122 | + | 15.6079i | 0.296287 | + | 0.513184i | ||||
\(926\) | −8.97742 | − | 5.18312i | −0.295016 | − | 0.170328i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.80397 | + | 6.58867i | 0.124871 | + | 0.216284i | ||||
\(929\) | 50.4538 | 1.65534 | 0.827668 | − | 0.561217i | \(-0.189667\pi\) | ||||
0.827668 | + | 0.561217i | \(0.189667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 9.84350 | + | 5.68315i | 0.322435 | + | 0.186158i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 31.4234 | + | 18.1423i | 1.02821 | + | 0.593635i | ||||
\(935\) | 7.88868 | − | 4.55453i | 0.257987 | − | 0.148949i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.6251i | 1.39250i | 0.717799 | + | 0.696250i | \(0.245150\pi\) | ||||
−0.717799 | + | 0.696250i | \(0.754850\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.22758 | − | 5.59033i | −0.105272 | − | 0.182336i | ||||
\(941\) | 55.0404 | 1.79427 | 0.897133 | − | 0.441761i | \(-0.145646\pi\) | ||||
0.897133 | + | 0.441761i | \(0.145646\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.32815i | − | 0.271202i | ||||||
\(944\) | 10.8659 | 0.353656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.8189 | −0.351752 | ||||||||
\(947\) | 25.6884i | 0.834760i | 0.908732 | + | 0.417380i | \(0.137052\pi\) | ||||
−0.908732 | + | 0.417380i | \(0.862948\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.03875 | −0.0986421 | ||||||||
\(950\) | −7.60248 | − | 13.1679i | −0.246657 | − | 0.427223i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3463i | 0.561903i | 0.959722 | + | 0.280952i | \(0.0906500\pi\) | ||||
−0.959722 | + | 0.280952i | \(0.909350\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.46279 | − | 0.844541i | 0.0473347 | − | 0.0273287i | ||||
\(956\) | 4.67039 | + | 2.69645i | 0.151051 | + | 0.0872094i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −20.0875 | − | 11.5975i | −0.648998 | − | 0.374699i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −90.0362 | −2.90439 | ||||||||
\(962\) | 1.82955 | + | 3.16887i | 0.0589870 | + | 0.102169i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.1233 | − | 6.99936i | −0.390464 | − | 0.225434i | ||||
\(965\) | 0.703935 | + | 1.21925i | 0.0226605 | + | 0.0392491i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.61334 | − | 4.52644i | 0.0840393 | − | 0.145560i | −0.820942 | − | 0.571011i | \(-0.806551\pi\) |
0.904981 | + | 0.425451i | \(0.139885\pi\) | |||||||
\(968\) | −6.86292 | + | 3.96231i | −0.220583 | + | 0.127353i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.13925 | − | 3.70529i | 0.0686873 | − | 0.118970i | ||||
\(971\) | −14.2195 | + | 24.6289i | −0.456326 | + | 0.790379i | −0.998763 | − | 0.0497167i | \(-0.984168\pi\) |
0.542438 | + | 0.840096i | \(0.317501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 24.8887 | − | 14.3695i | 0.797485 | − | 0.460428i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 1.09663i | − | 0.0351021i | ||||||
\(977\) | 24.3217i | 0.778119i | 0.921213 | + | 0.389059i | \(0.127200\pi\) | ||||
−0.921213 | + | 0.389059i | \(0.872800\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.55917 | − | 3.78694i | 0.209632 | − | 0.121031i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.1326 | − | 21.0143i | 0.387168 | − | 0.670595i | ||||
\(983\) | −13.4186 | + | 23.2417i | −0.427987 | + | 0.741295i | −0.996694 | − | 0.0812449i | \(-0.974110\pi\) |
0.568707 | + | 0.822540i | \(0.307444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.01222 | − | 1.16176i | 0.0641147 | − | 0.0370166i | ||||
\(986\) | −20.8182 | + | 36.0582i | −0.662987 | + | 1.14833i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.54353 | − | 2.67348i | −0.0491063 | − | 0.0850547i | ||||
\(989\) | −5.48446 | − | 3.16645i | −0.174396 | − | 0.100687i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.51093 | − | 6.08111i | −0.111528 | − | 0.193173i | 0.804858 | − | 0.593467i | \(-0.202241\pi\) |
−0.916387 | + | 0.400294i | \(0.868908\pi\) | |||||||
\(992\) | 11.0016 | 0.349303 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.99193 | + | 5.19149i | 0.285063 | + | 0.164581i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.60463 | + | 5.54524i | 0.304182 | + | 0.175619i | 0.644320 | − | 0.764756i | \(-0.277141\pi\) |
−0.340138 | + | 0.940375i | \(0.610474\pi\) | |||||||
\(998\) | 23.0209 | − | 13.2911i | 0.728713 | − | 0.420723i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2646.2.l.c.1097.5 | 48 | ||
3.2 | odd | 2 | 882.2.l.c.509.7 | 48 | |||
7.2 | even | 3 | 2646.2.m.c.881.15 | 48 | |||
7.3 | odd | 6 | 2646.2.t.c.2285.7 | 48 | |||
7.4 | even | 3 | 2646.2.t.c.2285.8 | 48 | |||
7.5 | odd | 6 | 2646.2.m.c.881.16 | 48 | |||
7.6 | odd | 2 | inner | 2646.2.l.c.1097.6 | 48 | ||
9.2 | odd | 6 | 2646.2.t.c.1979.7 | 48 | |||
9.7 | even | 3 | 882.2.t.c.803.24 | 48 | |||
21.2 | odd | 6 | 882.2.m.c.293.10 | yes | 48 | ||
21.5 | even | 6 | 882.2.m.c.293.3 | ✓ | 48 | ||
21.11 | odd | 6 | 882.2.t.c.815.13 | 48 | |||
21.17 | even | 6 | 882.2.t.c.815.24 | 48 | |||
21.20 | even | 2 | 882.2.l.c.509.6 | 48 | |||
63.2 | odd | 6 | 2646.2.m.c.1763.16 | 48 | |||
63.11 | odd | 6 | inner | 2646.2.l.c.521.6 | 48 | ||
63.16 | even | 3 | 882.2.m.c.587.3 | yes | 48 | ||
63.20 | even | 6 | 2646.2.t.c.1979.8 | 48 | |||
63.25 | even | 3 | 882.2.l.c.227.18 | 48 | |||
63.34 | odd | 6 | 882.2.t.c.803.13 | 48 | |||
63.38 | even | 6 | inner | 2646.2.l.c.521.5 | 48 | ||
63.47 | even | 6 | 2646.2.m.c.1763.15 | 48 | |||
63.52 | odd | 6 | 882.2.l.c.227.19 | 48 | |||
63.61 | odd | 6 | 882.2.m.c.587.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.l.c.227.18 | 48 | 63.25 | even | 3 | |||
882.2.l.c.227.19 | 48 | 63.52 | odd | 6 | |||
882.2.l.c.509.6 | 48 | 21.20 | even | 2 | |||
882.2.l.c.509.7 | 48 | 3.2 | odd | 2 | |||
882.2.m.c.293.3 | ✓ | 48 | 21.5 | even | 6 | ||
882.2.m.c.293.10 | yes | 48 | 21.2 | odd | 6 | ||
882.2.m.c.587.3 | yes | 48 | 63.16 | even | 3 | ||
882.2.m.c.587.10 | yes | 48 | 63.61 | odd | 6 | ||
882.2.t.c.803.13 | 48 | 63.34 | odd | 6 | |||
882.2.t.c.803.24 | 48 | 9.7 | even | 3 | |||
882.2.t.c.815.13 | 48 | 21.11 | odd | 6 | |||
882.2.t.c.815.24 | 48 | 21.17 | even | 6 | |||
2646.2.l.c.521.5 | 48 | 63.38 | even | 6 | inner | ||
2646.2.l.c.521.6 | 48 | 63.11 | odd | 6 | inner | ||
2646.2.l.c.1097.5 | 48 | 1.1 | even | 1 | trivial | ||
2646.2.l.c.1097.6 | 48 | 7.6 | odd | 2 | inner | ||
2646.2.m.c.881.15 | 48 | 7.2 | even | 3 | |||
2646.2.m.c.881.16 | 48 | 7.5 | odd | 6 | |||
2646.2.m.c.1763.15 | 48 | 63.47 | even | 6 | |||
2646.2.m.c.1763.16 | 48 | 63.2 | odd | 6 | |||
2646.2.t.c.1979.7 | 48 | 9.2 | odd | 6 | |||
2646.2.t.c.1979.8 | 48 | 63.20 | even | 6 | |||
2646.2.t.c.2285.7 | 48 | 7.3 | odd | 6 | |||
2646.2.t.c.2285.8 | 48 | 7.4 | even | 3 |